Question

24-1. In the text, we went from Equation 24.5 to 24.6 using a physical argument involving varying the size of the system while keeping T and P fixed. We could also have used a mathematical process called Euler's theorem. Before we can learn about Euler's theorem, we must first define a homogeneous function. A function f(z,, z,....) is said to be homogeneous if f(Az,.Az Az) = if(z,...Zy) Argue that extensive thermodynamic quantities are homogeneous functions of their exten- sive variables.

Answer 1

Page No We know thermodynamic functions are homogeneous in two - categories : » They are homogeneous to the Ist degree (1=1) and are - called Extensive functions. 2) They are homogeneous to the zeroth degree (d=0) and are called intensive functions. It means extensive thermodynamic quantilies like entropy can be written as homogeneous functions of their extensive variables. O eg:- The entropy (s) is completely described by three extensive variables: Internal energy, volume and number jele s- s (EVN) Nowor this extensive rasiable (ie ents-opy) can be represented by homogeneous , It degree function." Liwe call Write SCHE, OV, LAN) = AS CEĻ, N = D - Wherer Hol is called scaling function and it is arbitrary. . We choose = 1 , so equation 6 becomes : SE Ñ Ñ = LSCE, W, N) I Now, we introduce the internal energy per mole in E se and 1 Volume per mode in You = ste, 0, 1) = Is CE, V, N) Oh, Nisce, u, 1) - SCE,V, N whore, sce, 0, 1) is entropy per m ole This tells us that entropy of N moles of a substance is N times the entropy per mole of that substance. ing extensive thermodyna- mic quantities are homogeneous function of these extensive Variable